The Overview map doesn't have a way to bind to a custom extent, it automatically picks it up from the map control it is bind to. However, as a way around it, you could use a hidden map control, that does extent calculations from your original map control, on extent changed event handler and you can bind your overview map to that. A little bit tricky but might work.XAML:
<Grid x:Name="LayoutRoot">
<esri:Map x:Name="MyMap" Extent="-13631774.161,4551117.011,-13629848.904,4552046.199" ExtentChanged="MyMap_ExtentChanged">
<esri:ArcGISTiledMapServiceLayer ID="TopoLayer"
Url="http://services.arcgisonline.com/ArcGIS/rest/services/World_Topo_Map/MapServer"/>
</esri:Map>
<Grid HorizontalAlignment="Right" VerticalAlignment="Top" Width="300" Height="200" Canvas.ZIndex="100" >
<Border CornerRadius="0,0,0,10" Background="#BB919191">
<esri:OverviewMap x:Name="MyOverviewMap"
Margin="8,0,0,8"
Map="{Binding ElementName=MyMap_Ov}">
<esri:OverviewMap.Layer>
<esri:ArcGISTiledMapServiceLayer ID="StreetLayer"
Url="http://services.arcgisonline.com/ArcGIS/rest/services/World_Street_Map/MapServer"/>
</esri:OverviewMap.Layer>
</esri:OverviewMap>
</Border>
</Grid>
<esri:Map x:Name="MyMap_Ov">
<esri:ArcGISTiledMapServiceLayer ID="TopoLayer1"
Url="http://services.arcgisonline.com/ArcGIS/rest/services/World_Topo_Map/MapServer"/>
</esri:Map>
</Grid>
XAML.CS
private void MyMap_ExtentChanged(object sender, ESRI.ArcGIS.Client.ExtentEventArgs e)
{
MyMap_Ov.Visibility = System.Windows.Visibility.Collapsed;
MyMap_Ov.Extent = MyMap.Extent.Expand(4);
}